Question

I missed a lesson today on factoring and was wondering if i can get some help here

for example, let's use 2x^2+5x+3

Answer 1

There are several ways.
The method that for some reason seems to be the most popular
these days is "decomposition"
In that method, multiply the coefficients of the x^2 term and the constant
.... (2)(3) = 6
Now look for factors of 6 that have a sum of +5
1,6 ---- 7 no
2,3 ---- 5 , got it!

now replace the 5x with 2x+3x
2x^2 + 2x + 3x + 3
factor in pairs:
2x(x+1) + 3(x+1)
now you have a common factor of x+1
= (x+1)(2x+3)
and there you have it!!!

Answer 2

Here is another example, a bit more complicated
8x^2 - 14x - 15
--- (8)(-15) = -120

factors:
-1,120 ---sum--- 119 , no
-2,60 ---sum--- 58
-4,30 ---sum--- 26
-5,24 ---sum--- 19
-6, 20 ---sum--- 14 , but 6,-20 has a sum of -14

8x^2 - 14x - 15
= 8x^2 - 20x + 6x - 15, if the signs are mixed I place the negative term first
= 4x(2x - 5) + 3(2x - 5)
= (2x - 5)(4x + 3)

Answer 3

Reiny, that was an excellent explanation!!